Question

A collection of coins consisting of 10-cent, 20-cent and 50-cent pieces has a value of $4.50. The number of 20-cent pieces is twice the number of 10-cent pieces and the number of 50-cent pieces is 3 less than twice the number of 10-cent pieces. How many 10-cent, 20-cent and 50-cent pieces are there in the collection?

Answer 1

let's define everything in terms of the number of 10 cent coins, and then just translate the English into Math.

let the number of 10 cent coins be x
"The number of 20-cent pieces is twice the number of 10-cent pieces"
--> number of 20 cent pieces = 2x
"the number of 50-cent pieces is 3 less than twice the number of 10-cent pieces"
--> number of 50 cent pieces = 2x - 3

now taking in the values of the coins

10x + 20(2x) + 50(2x-3) = 450
10x + 40x + 100x- 150 = 450
150x = 600
x = 4

So there are 4 ten-cent coins
8 twenty-cent coins and
5 fifty-cent coins

check:
4(10) + 8(20) + 5(50)
= 40 + 160 + 250
= 450 cents
= $4.50